本文選題：分?jǐn)?shù)階Laplace + 特征值　； 參考：《蘭州大學(xué)》2017年碩士論文

【摘要】：微分算子是線性算子中最基本的一類無界算子,在數(shù)學(xué)物理以及其他學(xué)科中都有廣泛的作用.線性微分算子的特征值和特征函數(shù)是算子理論的核心之一,也是研究相應(yīng)的非線性問題的基礎(chǔ).本文討論了有界區(qū)域上權(quán)函數(shù)變號(hào)的分?jǐn)?shù)階Laplace算子特征值問題(?)特征值和特征函數(shù)的性質(zhì).得到上述問題一列特征值序列的存在,尤其證明了第一特征值λ1,是簡單的.緊接著在對(duì)權(quán)函數(shù)g(x)為有界可測(cè)的假設(shè)下,討論了特征值所對(duì)應(yīng)的正的特征函數(shù)的存在性,所得到的結(jié)論縮小了非負(fù)特征函數(shù)對(duì)應(yīng)的特征值的范圍,這些結(jié)果推廣了Yang等人[Int. J. Bifur. Chaos. 2015],Servadei 等人[Discrete Contin. Dyn. Syst. 2013]及 Brown等人[J. Math. Anal.Appl. 1980]的主要結(jié)果.
[Abstract]:Differential operators are the most basic class of unbounded operators in linear operators, which play a wide role in mathematics, physics and other disciplines. The eigenvalues and eigenfunctions of linear differential operators are the core of operator theory and the basis of studying the corresponding nonlinear problems. In this paper, we discuss the eigenvalue problem of fractional Laplace operator on bounded domain. The properties of eigenvalues and eigenfunctions. The existence of a sequence of eigenvalues is obtained, especially the first eigenvalue 位 1 is proved to be simple. Then the existence of positive eigenfunctions corresponding to eigenvalues is discussed under the assumption that the weight function gx is bounded and measurable. The results obtained reduce the range of eigenvalues corresponding to non-negative eigenfunctions. These results generalize Yang et al. [Int.] J. Bifur. Chaos. 2015. Dyn. Syst. Brown et al. [J. Math. Anal.Appl. 1980.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175.3

【參考文獻(xiàn)】

相關(guān)博士學(xué)位論文 前1條

1 楊變霞;分?jǐn)?shù)階Laplace算子的譜理論及其在微分方程中的應(yīng)用[D];蘭州大學(xué);2015年

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本文編號(hào)：2045477